ESTIMATION OF DENSITY AND DISTRIBUTION FUNCTIONS OF A BURR X DISTRIBUTION

Abstract

Burr type X distribution is one of the members of the Burr family which was originally
derived by Burr (1942) and can be used quite effectively in modelling strength data and
also general lifetime data. In this article, we consider efficient estimation of the probability
density function (PDF) and cumulative distribution function (CDF) of Burr X distribution.
Eight different estimation methods namely maximum likelihood estimation,
uniformly minimum variance unbiased estimation, least square estimation, weighted least
square estimation, percentile estimation, maximum product estimation, Crem´er-von-Mises
estimation and Anderson-Darling estimation are considered. Analytic expressions for bias
and mean squared error are derived. Monte Carlo simulations are performed to compare
the performances of the proposed methods of estimation for both small and large samples.
Finally, a real data set has been analyzed for illustrative purposes.